Gaffer Tape said:

I actually think cutnshut is right in saying that Vader has no character development in ESB. He stays exactly the same throughout. One might argue that he had character development occur offscreen in between Star Wars and ESB when he finds out that his son is alive and working for the Rebels. But at the beginning of ESB, he has a singular mission in mind. He works towards that singular goal for the entire film. He confronts that goal in the end. He fails to achieve that goal, and we're left assuming that he will continue in some capacity to achieve that goal. But no deviation ever occurs, no second thoughts of any kind.

I guess it depends on how you define character development? I think Vader's rage subtly increases during the runtime, opposite of the length of his patience. You're right, the biggest changes occur in the untold gap between the end of ANH and the start of ESB, but I don't think you can say that he's the same throughout ESB. Especially considering the end of the movie. Not the reveal as much, although I think that counts for something... but how he acts after the reveal. Vader during the rest of the movie is working like a man possessed of a single goal, and grows more and more impatient with incompetance the longer it takes to make it happen. However, after finally making contact with his son, he's a changed man. The burden of finding his son... the ball is no longer in his court. He's done what he set out to do. It's comparable to the change between Han & Leia after they stop fighting and pretending to not be a couple, and admit that they are a couple.

You wouldn't say Han or Leia is unchanging in the movie, just because they are rebels at the beginning and rebels at the end, right? There's more to "character arc" than what colour your hat is, right?